The Use of a Hidden Mixture Transition Distribution Model in Clustering Few but Long Continuous Sequences: An Illustration with Cognitive Skills Data

Zhivko Taushanov,Paolo Ghisletta

doi:10.3390/sym12101618

Abstract

In accordance with the theme of this special issue, we present a model that indirectly discovers symmetries and asymmetries between past and present assessments within continuous sequences. More specifically, we present an alternative use of a latent variable version of the Mixture Transition Distribution (MTD) model, which allows for clustering of continuous longitudinal data, called the Hidden MTD (HMTD) model. We compare the HMTD and its clustering performance to the popular Growth Mixture Model (GMM), as well as to the recently introduced GMM based on individual case residuals (ICR-GMM). The GMM and the ICR-GMM contrast with HMTD, because they are based on an explicit change function describing the individual sequences on the dependent variable (here, we implement a non-linear exponential change function). This paper has three objectives. First, it introduces the HMTD. Second, we present the GMM and the ICR-GMM and compare them to the HMTD. Finally, we apply the three models and comment on how the conclusions differ depending on the clustering model, when using a specific dataset in psychology, which is characterized by a small number of sequences (n = 102), but that are relatively long (for the domains of psychology and social sciences: t = 20). We use data from a learning experiment, in which healthy adults (19–80 years old) were asked to perform a perceptual–motor skills over 20 trials.

Highlights

A major goal of developmental science is to describe how individuals change in time, to or differently from each other [1]
Below, we show the results of the ICR-Growth Mixture Model (GMM) and of GMM based on the three-parameter exponential change function presented in Equation (1)
We briefly discussed each of the three methods that we find well-suited for sequences of continuous data: GMM, ICR-GMM, and Hidden MTD (HMTD)

Summary

Introduction

A major goal of developmental science is to describe how individuals change in time, to or differently from each other [1]. Change phenomena are often studied with growth models and similar techniques. These consist of statistical models for describing both within-person change and between-person differences that are based on mathematical change functions with interpretable parameters [2]. The main advantage of this approach is that the nature of the parameters across the clusters can help for the substantive interpretation of the change phenomenon under investigation. This approach can yield problems, such as the overextraction of clusters [3]

Methods

Results

Discussion

Conclusion